Convergence Rates for Residual Branching Particle Filters

نویسنده

  • Michael A. Kouritzin
چکیده

A large class of proven discrete-time branching particle filters with Bayesian model selection capabilities and effective resampling is analyzed mathematically. The particles interact weakly in the branching procedure through the total mass process in such a way that the expected number of particles can remain constant. The weighted particle filter, which has no resampling, and the fullyresampled branching particle filter are included in the class as extreme points. Otherwise, selective residual branching is used allowing any number of offspring. Each particle filter in the class is coupled to a McKean-Vlasov particle system, corresponding to a reduced, unimplementable branching particle filter, for which Marcinkiewicz strong laws of large numbers (Mllns) and the central limit theorem (clt) can be written down. Coupling arguments are used to show the reduced system can be used to predict performance of and to transfer the Mllns to the real weakly-interacting residual branching particle filter. This clt is also shown transferable when (a few) extra particles are used. MSC 2010 subject classifications: Primary 60F05, 60G35; secondary 62M20, 60G09, 62E20, 60J80.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Rates for Branching Particle Approximations of Continuous - Discrete Filters

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measure-valued process t→ μt(·) . = P{Xt ∈ ·|σ{Ytk , tk ≤ t}}, where tk = kε and Ytk is a distorted, corrupted, partial observation of Xtk . Then, one constructs a particle system with observat...

متن کامل

Residual and stratified branching particle filters

A class of discrete-time branching particle filters is introduced with individual resampling: If there are Nn particles alive at time n, N0 = N , an ≤ 1 ≤ bn, L̂n+1 is the current unnormalized importance weight for particle i and An+1 = 1 N Nn ∑ i=1 L̂n+1, then weight is preserved when L̂n+1 ∈ (anAn+1, bnAn+1). Otherwise, ⌊ L̂in+1 An+1 ⌋ +ρn offspring are produced and assigned weight An+1, where ρn...

متن کامل

A Branching Particle Approximation to the Filtering Problem with Counting Process Observations∗

Recently, the filtering model with counting process observations has been demonstrated as a sensible framework for modeling the micromovement of asset price (or ultra-high frequency data). In this paper, we first construct a branching particle system for such a nonlinear filtering model. Then, we show the weighted empirical measures in the constructed branching system converges to the optimal f...

متن کامل

Particle Approximations to the Filtering Problem in Continuous Time

In this chapter, we survey some recent results on the particle system approximations to stochastic filtering problems in continuous time. First, a weighted particle system representation of the optimal filter is given and a numerical scheme based on this representation is proposed. Its convergence to the optimal filter, together with the rate of convergence is proved. Secondly, to reduce the es...

متن کامل

On Convergence of Particle Filters with General Importance Distributions

This paper is concerned with convergence of particle filter estimates of unbounded functions with general importance distributions. Particle filters are numerical methods for approximating Bayesian filtering solutions of non-linear/non-Gaussian state space models using sequential importance sampling. The performance of particle filters heavily depends on how the importance distribution for the ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016